A margin against a fracture is determined in general using a thinning criterion or a forming limit diagram (FLD). The FLD indicates the major and minor strain (ε1 and ε2, respectively) at which the failure generally occurs, and can be used in a crash analysis. The FLD can be experimentally determined by loading specimens along various proportional paths. Nakazima et al., for example, describes an operation of hemispherical punch stretching for rectangular specimens with various widths. Before the forming operation, small circulars or grids are marked on the sheet surface by etching or printing. Theses circles are generally distorted into ellipses during the forming operation, which will be terminated at the onset of necking or crack. The size of an ellipse near the neck likely varies with the width of the specimen. The major and minor strains can be measured from the ellipse at the neck or crack. Finally, the forming limit curve (FLC) is drawn so that it fits the measured limit strains for various paths.
FIG. 1 shows an exemplary fracture limit curve measured by experiment. As an FLD prediction method, there may be a combined usage of Hill's criterion and Swift's one, Marciniak-Kuczynski model, Storen-Rice model, etc., and the FLD can be obtained by correcting the influence of a sheet thickness by a Keeler's empirical rule. The tearing can be produced by a dynamic FE code, whereas the former may not be detected in the FE analyses. Instead of direct predictions of the tearing, the computed strains are likely compared with critical values external prepared and it is regarded that the failure occurs when one of the computed strains reaches the limit. Certain additional documents which may be relevant to the technology described herein include CAMP-ISIJ17, 1063, 2004; and Metal Forming, Hosford, 319, 1993.